Mathematics for the Million - Lancelot Hogben ***

This is one of the strangest maths books you are ever likely to encounter. Written in the 1930s and reissued in 2017, it's an attempt to provide mathematical instruction up to around A-level standard (though obviously the curriculum has changed a lot) for someone who, perhaps, doesn't respond well to the classroom and works better from self-teaching.

It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation.

Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more.

The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.

Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.

It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies.

To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.

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Review by Brian Clegg

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